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All commonly used formulas for geometric objects are really mathematical models of the characteristics of physical objects. For example, the characteristic of the volume inside a common closed cardboard box can be modeled by the formula for the volume of a rectangular solid, V = L x W x H, where L = Length, W = Width, and H = Height of the box. A basketball, because it is a sphere, can be partially modeled by its distance from one side through the center to the other side, or diameter, by the diameter formula for a sphere, D = 2r.2. (Please review Chapter 9 in the College Math text for geometric objects and their properties; walls, windows, and ceilings are all rectangles.) The walls and ceiling in your bedroom need to be painted, and the painters’ estimates to do the work are far too expensive. You decide that you will paint the bedroom yourself. The bedroom is 14 ft. 3 in. by 16 ft., and the ceiling is 8 ft. high. The color of paint you have selected covers 75 sq. ft. per gallon, and costs $33.50 per gallon. The ceiling will be painted with a bright white ceiling paint that costs $28.50 per gallon but only covers 50 sq. ft. per gallon. There is one window in the room, and it is 3 ft. 4 in. by 5 ft. and will not be painted. The inside of the bedroom door is to be painted the same color as the walls. Describe and discuss how you will use Polya’s problem-solving techniques to determine how much it will cost to paint this room with two coats of paint (on both walls and ceiling). Then, using your solution strategy, determine how much it will actually cost to paint your bedroom. Assuming you can paint 100 sq. ft. per hour, what will be the work time needed to paint your bedroom? (Because different paint lots of the same color may appear slightly different colors, when painting a room, you should buy all of your paint at one time and intermix the paint from at least two different cans so that the walls will all be exactly the same color.)

Stats Quiz 4*The lifetimes of light bulbs of a particular type are normally distributed with a mean of 270 hours and a standard deviation of 11 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?Apply the 68-95-99.7 rule to this questions. A. 68% B. 1005 C. 99.7% D. 95%*The annual precipitation for one city is normally distributed with a mean of 72 inches and a standard deviation of 3.5 inches. Fill in the blanks.In 99.7% of the years, the precipitation in this city is between __________ and __________ inches. Apply the 68-95-99.7 rule to this questions.A. 61.5, 82. 5 B. 82.5, 61.5 C. 61.5, 85.5 D. 63.5, 82.5*A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 225 and 275. A. 0.2416 B. 0.2418 C. 0.2417 D. 0.2420

A. Identify the objective function.1. Determine the total profit to be made if the company produces a combination of cases of Brand X and Brand Y that lies on the black-dashed objective function line (profit line), as shown on the graph in the attached “QAT1 Task 2 Spreadsheet.”B. Write the four constraints that are described in the scenario given in the attached “QAT1 Task 2 Spreadsheet.”1. Describe why each of the four written constraints from part B is a minimum or a maximum constraint.C. Analyze the optimum production yielding the greatest amount of profit by doing the following:1. Determine the number of cases of Brand X that should be produced, showing all of your work.2. Determine the number of cases of Brand Y that should be produced, showing all of your work.3. Discuss how the feasible region was used to arrive at your calculations for parts C1 and C2.4. Determine the total profit that would be generated by the production levels determined in parts C1 and C2, showing all of your w

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